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Basic Proportionality Theorem

15. ABCD is a...

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15. ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced atQ. prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC.

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ABCD is a parallelogram and APQ is a straight line meeting BC at Pend DC produced at Q. prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC.

$In the given figure, ABCD is a quadrilateral in which A B | | D C and P is the midpoint of BC. On producing, AP and DC meet at Q. Prove that (i) AB = CQ, (ii) DQ = DC + AB.$

Q. In parallelogram

A B C D

E

is the mid-point at

A B

A P

E C

D C

O

B C

P

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(I)

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A P

Q. ABCD is a parallelogram, AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC

In the adjoining figure ABCD is a parallelogram. ‘P’ is a point on BC, DP and AB are produced meet at L. Prove that DP : PL = DC : BL.

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